Which one is correct?
- You need you and your partner's documents.
- You need your and your partner's documents.
Also, am I safe to assume that the following version is certainly wrong?
- You need yours and your partner's documents.
In my strong opinion, from all the above sentences the only grammatically correct is
You need your and your partner's documents.
Although I would put it:
You need your partner's and your documents.
To test it, you may take away "(and) your partner's"):
You need your documents. (correct)
*You need yours documents. (incorrect)
*You need you documents. (incorrect)
Your sentence #2 and #3 are correct. But sentence #1 is grammatically wrong (if you only mean the documents). Please read on for explanation as to why I say your first sentence is wrong.
I saw a blue bird and a yellow bird.
The word "and" is a co-ordinator. What it does is coordinate two constituents of equal status. Coordination is a non-headed construction, unlike Noun Phrase, Verb Phrase etc. The coordination here is - "a blue bird and a yellow bird".
In the quoted sentence above the constitutes are - "a blue bird" and "and a yellow bird". We call the first constituents a bare coordinates and the second a expanded coordinates.
This two coordinates have equal status in the clause where it occurs. Both of them are the objects of the sentence. You can drop any one constituents without risking the sentence to be ungrammatical.
Here coordination occurs between two Noun Phrases. In the following sentence it is not the case -
I saw a blue and yellow bird.
Notice that here the coordination occurs between two modifiers (equal status). And thus form a larger Adjective Phrase - "blue and yellow".
The meaning changes here. In the first quoted sentence I saw two birds. One bird is blue and the other bird is yellow. In the second sentence I saw only one bird, which has both blue and yellow colour on its body.
In your sentence -
I need you and your partner's documents.
Here "and" coordinates two constituents that doesn't have the same status, unless you mean that I need you (a person) and a document.
[While discussing about your sentence I changed the subject "you" to "I" for clarity.]